Ampere-Maxwell Law quiz with answers and explanations

📚 Quick Study Guide

• 🧲 Ampere's Law relates magnetic fields to electric currents producing them: $\oint B \cdot dl = \mu_0 I_{enc}$
• ⚡️ Maxwell's addition introduced the concept of displacement current ($I_d$) due to changing electric fields: $I_d = \epsilon_0 \frac{d\Phi_E}{dt}$
• 💡 Ampere-Maxwell Law combines both: $\oint B \cdot dl = \mu_0(I_{enc} + I_d)$
• 📐 $\Phi_E$ represents the electric flux, the electric field passing through a given area.
• ✨ $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} T \cdot m/A$).
• ⏱️ The changing electric field acts as a source of magnetic field, just like a real current.
• 📝 The law is crucial for understanding electromagnetic waves.

🧪 Practice Quiz

1. Which of the following best describes Ampere-Maxwell's Law?
   1. The relationship between electric field and current.
   2. The relationship between magnetic field and current, modified to include changing electric fields.
   3. The relationship between electric and magnetic fields in free space.
   4. The force between two current-carrying wires.
2. What is the significance of the displacement current introduced by Maxwell?
   1. It explains the flow of electrons in a circuit.
   2. It accounts for the magnetic field produced by a changing electric field.
   3. It corrects Ampere's Law for static magnetic fields.
   4. It describes the polarization of dielectrics.
3. In the Ampere-Maxwell Law, what does the term $\oint B \cdot dl$ represent?
   1. The electric flux through a surface.
   2. The magnetic flux through a surface.
   3. The line integral of the magnetic field around a closed loop.
   4. The surface integral of the magnetic field.
4. What is the role of $\epsilon_0$ in the displacement current term?
   1. It represents the magnetic permeability of free space.
   2. It represents the electric permittivity of free space.
   3. It represents the charge of an electron.
   4. It represents the speed of light.
5. If there is a changing electric field but no conduction current, what does Ampere-Maxwell's Law predict?
   1. There will be no magnetic field.
   2. There will be a magnetic field due to the displacement current.
   3. There will be an electric field only.
   4. The law is not applicable in this situation.
6. Which of the following phenomena is best explained by Ampere-Maxwell's Law?
   1. Electrostatic forces.
   2. Electromagnetic induction.
   3. The propagation of electromagnetic waves.
   4. The photoelectric effect.
7. How does Maxwell's addition to Ampere's Law resolve the inconsistency in Ampere's Law when dealing with charging capacitors?
   1. It replaces the conduction current with the displacement current between the capacitor plates.
   2. It ignores the current between the capacitor plates.
   3. It doubles the effect of the magnetic field.
   4. It uses a different value for permeability.